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Starting with the pioneering work of Ein and Lazarsfeld restrictions onvalues of Seshadri constants on algebraic surfaces have been studied by manyauthors. In the present note we show how approximation involving continuedfractions combined with recent results of Kuronya and Lozovanu on Okounkovbodies of line bundles on surfaces lead to effective statements considerablyrestricting possible values of Seshadri constants. These results in turnprovide strong aditional evidence to a conjecture governing the Seshadriconstants on algebraic surfaces with Picard number 1.

Restrictions on Seshadri constants on surfaces